出力

入力例 1

出力例 1

入力例 2

出力例 2

入力例 3

出力例 3

1999999680

入力例 4

5
123456 789012
123 456
12 345678901
123456 789012
1 23

出力例 4

246433

入力例 5

1
1 400

出力例 5

0

Score : 1000 points

Problem Statement

AtCoDeer the deer found N rectangle lying on the table, each with height 1.
If we consider the surface of the desk as a two-dimensional plane, the i-th rectangle i(1≤i≤N) covers the vertical range of [i-1,i] and the horizontal range of [l_i,r_i], as shown in the following figure:

AtCoDeer will move these rectangles horizontally so that all the rectangles are connected.
For each rectangle, the cost to move it horizontally by a distance of x, is x.
Find the minimum cost to achieve connectivity.
It can be proved that this value is always an integer under the constraints of the problem.

Constraints

All input values are integers.

1≤N≤10^5

1≤l_i<r_i≤10^9

Partial Score

300 points will be awarded for passing the test set satisfying 1≤N≤400 and 1≤l_i<r_i≤400.